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1、GraduateTextsinMathematics258EditorialBoardS.AxlerK.A.RibetForothertitlespublishedinthisseries,gotowww.springer.com/series/136OsmanGülerFoundationsofOptimizationOsmanGülerDepartmentofMathematics&StatisticsUniversityofMaryland,BaltimoreCountyHilltopCircle1000Baltimore,MD212
2、50USAguler@umbc.eduEditorialBoard:S.AxlerK.A.RibetMathematicsDepartmentMathematicsDepartmentSanFranciscoStateUniversityUniversityofCaliforniaatBerkeleySanFrancisco,CA94132Berkeley,CA94720USAUSAaxler@sfsu.eduribet@math.berkeley.eduISSN0072-5285ISBN978-0-387-34431-7e-ISBN978
3、-0-387-68407-9DOI10.1007/978-0-387-68407-9SpringerNewYorkDordrechtHeidelbergLondonLibraryofCongressControlNumber:2010932783MathematicsSubjectClassification(2010):90-01,90C30,90C46,90C25,90C05,90C20,90C34,90C47,49M37,49N15,49J53,49J50,49M15,49K35,65K05,65K10,52A05,52A07,52A
4、35,52A41,52A40,52A37©SpringerScience+BusinessMedia,LLC2010Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermissionofthepublisher(SpringerScience+BusinessMedia,LLC,233SpringStreet,NewYork,NY10013,USA),exceptforbriefexcerptsinconnectionw
5、ithreviewsorscholarlyanalysis.Useinconnectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarte
6、rms,eveniftheyarenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprietaryrights.Printedonacid-freepaperSpringerispartofSpringerScience+BusinessMedia(www.springer.com)Idedicatethisbooktomymother,Z•ul yeG•uler,andtothememoryofmyfath
7、er,EsrefG•uler.PrefaceOptimizationiseverywhere.Itishumannaturetoseekthebestoptionamongallthatareavailable.Nature,too,seemstobeguidedbyoptimization
8、manylawsofnaturehaveavariationalcharacter.Amonggeometric guresintheplanewitha xedperimeter,thecirclehasthegreatestarea.Suchis
9、operimet-ricproblemsinvolvinggeometric guresdatebacktoancientGreece.Fermat'sprinciple,dis
